The degree of a distribution \(T\in \mathcal {D}^{\prime }(\Omega -O)\)  with respect to \(O\)  is similarly defined. Consider a distribution \(T\in \mathcal {D}^{\prime }(\Omega -O)\)  such that \(T(\psi )=\int _{\Omega -O} f\psi \operatorname{da}\)  for all \(\psi \in \mathcal {D}(\Omega -O)\)  and \(|f(x)|\le c_0 |x|^m\)  in a neighbourhood of \(O\) . Then \(\operatorname{deg}(T)\le -m-2\) . The degree of a distribution, which is locally integrable in \(\Omega -O\) , describes the order of the function at point \(O\) . For any distribution \(T\in \mathcal {D}^{\prime }(\Omega ),\)  we have \(\operatorname{deg}(\partial ^\alpha T)<\operatorname{deg}(T)+|\alpha |\)  for any multi index \(\alpha \in \mathbb {N}^2\) . For a given distribution \(T\in \mathcal {D}^{\prime }(\Omega -O)\)  the notion of degree of distribution controls the existence and uniqueness of extension \(\bar{T} \in \mathcal {D}^{\prime }({\Omega })\)  of \(T\)  [1]}. For instance, for a distribution \(T\in \mathcal {D}^{\prime }(\Omega -O)\) , with a negative degree of divergence, i.e., \(\operatorname{deg}(T)<0\) , there exists a unique extension \(\bar{T} \in \mathcal {D}^{\prime }(\Omega )\)  such that \(\bar{T}|_{\Omega -O}=T\)  [2]}. Several other properties of the degree of a distribution are discussed elsewhere [1]}, [2]}.
